The battle for Sprint that ended last week amounted to three-dimensional corporate chess with the four players — Sprint, SoftBank, Dish and Clearwire — making multiple, head-spinning moves.

One observer noted that any one of five outcomes couldn’t be discounted: Sprint buys Clearwire and SoftBank buys Sprint; Dish buys Sprint and Clearwire; Dish takes a minority stake in Clearwire; Sprint lets Dish have Clearwire; or SoftBank walks away.

Analyst Kevin Manning of BMO Capital Markets Corp., told Mark Davis, The Star’s business reporter covering the deal: “This has been one of the most bizarre corporate transactions I’ve seen to date.”

For Sprint, it’s turning out well.

Sprint and CEO Dan Hesse succeeded in entering the welcoming embrace of the stronger-financed SoftBank.

Sprint will still be looking a long way up at industry behemoths AT&T and Verizon. But the Wall Street Journal reported that in Sprint’s latest proxy filing the company now projects capital investment in its network of $20 billion over next two years. According to FactSet, that’s 21 percent more than the analysts had estimated.

And next week, Sprint will make the final winning move for Clearwire.

As for Toyko-based SoftBank, its $21.6 billion for 78 percent of Sprint nails down the biggest purchase of an overseas company by a Japanese company ever. And billionaire CEO Masayoshi Son moves forward with the 300-year plan for his company.

What made the game for Sprint a nail-biter was that SoftBank and Sprint had to stave off the late and higher but more debt-laden bid by Dish and its billionaire CEO, Charlie Ergen.

This really was a battle between billionaires.

Ergen’s incursion, however, did bring out the true value on what turned out to be the crown jewel in the whole deal: Clearwire and its load of spectrum.

Sprint already owned half of Clearwire and had wanted to buy up the rest, even before SoftBank came calling last fall. And Dish had tried but failed to work out a deal for some of Clearwire’s spectrum early this year.

SoftBank, Sprint and Dish all recognized that Clearwire’s spectrum — high-frequency spectrum that doesn’t travel very far — had been underused given the increase of mobile devices in dense urban areas. It’s also compatible with SoftBank devices.

The Dish bid for Sprint essentially went nowhere. But Dish intensified the battle for Clearwire, making a tender offer for Clearwire shares that, at $4.40 a share, topped the SoftBank-Sprint offer by a buck.

If there was any misstep by SoftBank-Sprint, that was it. They tried to make off with the Clearwire on the cheap, and eventually had to up their bid to $5 a share.

That $5 bid will stand up, and last week Dish dropped out of the game.

Dish’s overall strategy throughout appeared confusing. In making its bid for Sprint, it said it wanted to sell its satellite TV service with Sprint’s cell phone service. That may have been a market advantage in rural areas with less access to cable TV, but that synergy wouldn’t have mattered so much in cities.

Yet in the end, it appeared that all Dish really, really wanted was Clearwire’s city-friendly spectrum.

It will be interesting to see whether Sprint and Dish would now work on cutting a friendlier deal to give Dish access to some of that spectrum.

So despite the bizarreness of it all, or maybe because of it, it’s still possible that in the best American business tradition everybody might walk away with something: SoftBank with Sprint and Clearwire, Dish with some access to that Clearwire spectrum.

But there’s an intangible here, something that Sprint walks away with: Masayoshi Son showed that in winning the game for Sprint, he’ll bring a ton of confidence and moxie to the battle with Verizon, AT&T and T-Mobile.

As he said a couple of weeks ago: “You are not lucky to be my competitor.”